# Revisiting Euler-Angle Regression with Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2607.09650 · HTML: https://mlsanity.com/paper/2607.09650/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 30 of 34)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [HybrIK: A Hybrid Analytical-Neural Inverse Kinematics Solution for 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2011.14672/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [FreiHAND: A Dataset for Markerless Capture of Hand Pose and Shape from Single RGB Images](https://mlsanity.com/paper/1909.04349/) (2019)
- [Perpetual Humanoid Control for Real-time Simulated Avatars](https://mlsanity.com/paper/2305.06456/) (2023)
- [DeepCap: Monocular Human Performance Capture Using Weak Supervision](https://mlsanity.com/paper/2003.08325/) (2020)
- [Cameras as Rays: Pose Estimation via Ray Diffusion](https://mlsanity.com/paper/2402.14817/) (2024)
- [Neural Kinematic Networks for Unsupervised Motion Retargetting](https://mlsanity.com/paper/1804.05653/) (2018)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [Dyn-HaMR: Recovering 4D Interacting Hand Motion from a Dynamic Camera](https://mlsanity.com/paper/2412.12861/) (2024)
- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [Object-Centric Dexterous Manipulation from Human Motion Data](https://mlsanity.com/paper/2411.04005/) (2024)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [PhysPT: Physics-aware Pretrained Transformer for Estimating Human Dynamics from Monocular Videos](https://mlsanity.com/paper/2404.04430/) (2024)
- [From Skin to Skeleton: Towards Biomechanically Accurate 3D Digital Humans](https://mlsanity.com/paper/2509.06607/) (2025)
- [Reconstructing Humans with a Biomechanically Accurate Skeleton](https://mlsanity.com/paper/2503.21751/) (2025)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [Body Knowledge and Uncertainty Modeling for Monocular 3D Human Body Reconstruction](https://mlsanity.com/paper/2308.00799/) (2023)
- [From Kepler to Newton: Inductive Biases Guide Learned World Models in Transformers](https://mlsanity.com/paper/2602.06923/) (2026)
- [Weakly-Supervised 3D Hand Reconstruction with Knowledge Prior and Uncertainty Guidance](https://mlsanity.com/paper/2407.12307/) (2024)
- [Diffusion-based 3D Hand Motion Recovery with Intuitive Physics](https://mlsanity.com/paper/2508.01835/) (2025)
- [Face-from-Depth for Head Pose Estimation on Depth Images](https://mlsanity.com/paper/1712.05277/) (2017)
- [PAD-Hand: Physics-Aware Diffusion for Hand Motion Recovery](https://mlsanity.com/paper/2603.26068/) (2026)
- [Learning Unorthogonalized Matrices for Rotation Estimation](https://mlsanity.com/paper/2312.00462/) (2023)

## Abstract (arXiv)

In many real-world systems, including articulated robots and biomechanical models, rotations are defined in joint space and naturally parameterized by Euler angles with bounded ranges. Yet regressing Euler angles remains challenging, as their discontinuities and singularities often destabilize training. In this work, we revisit Euler-angle regression and show that its effectiveness depends critically on the interaction between rotation representation, regression architecture, and domain constraints. We introduce a new framework that combines range-aware Euler modeling with Kolmogorov-Arnold Networks (KAN), which replace fixed node-wise activations with learnable univariate functions on edges. We further provide theoretical analysis indicating that bounded Euler ranges motivate a near-additive structure in the regression function, which favors the additive functional form of KAN, and we confirm this trend empirically. Extensive experiments on controlled rotation regression, object pose estimation, and robotic and human inverse kinematics demonstrate consistent improvements in accuracy, convergence, and efficiency. The code will be publicly available.